Answer
The equation of the line that passes through the point $\left( -2,6 \right)$ and is perpendicular to the line $x=-4$ is $y=6$.
Work Step by Step
The line $x=-4$ is a vertical line with undefined slope.
The horizontal line has a slope of zero and is perpendicular to the vertical line.
Thus, the slope of the line perpendicular to the line $x=-4$ is 0.
Substitute the value of the slope of the line $m=0$ and point $\left( {{x}_{1}},{{y}_{1}} \right)=\left( -2,6 \right)$ in the equation $y-{{y}_{1}}=m\left( x-{{x}_{1}} \right)$.
$\begin{align}
& y-6=\left( 0 \right)\left( x-\left( -2 \right) \right) \\
& y-6=0 \\
& y=6
\end{align}$
Thus, the required equation of the line is $y=6$.
